FIG. 1 shows a cross-section of a conventional buried-ridge AlGaAs semiconductor laser device. The device includes an N-side electrode 1 disposed on one surface of an N-type GaAs substrate 2. An N-type Al.sub.x Ga.sub.1-x As first cladding layer 3 is disposed on the opposite surface of the GaAs substrate 2. A P-type or undoped intrinsic Al.sub.y Ga.sub.1-y As active layer 4 is disposed on the first cladding layer 3. A P-type Al.sub.x Ga.sub.1-x As second cladding layer 5 with a centrally located ridge 51 is disposed on the active layer 4. The second cladding layer 5 is formed by first forming a P-type Al.sub.x Ga.sub.1-x As layer having a given thickness on the active layer 4 and removing portions of the thus formed P-type Al.sub.x Ga.sub.1-x As layer by photolithographic and etching techniques to thereby leave in a center portion of the layer the ridge 51 which extends in the direction along a laser resonator. An N-type GaAs current blocking layer 7 is formed on the removed portions to bury the ridge 51 in the current blocking layer 7. Over the ridge 51 of the second cladding layer 5 and the current blocking layer 7, a P-type GaAs contact layer 8 is disposed, and a P-side electrode 9 for current injection is disposed on the P-type GaAs contact layer 8.
In FIG. 2, a current flow model for the conventional buried-ridge semiconductor laser device of FIG. 1 is shown. This current flow model has been prepared based on an article, "A GaAs-Al.sub.x Ga.sub.1-x As Double Heterostructure Planar Stripe Laser" by Yonezu et al in Japanese Journal of Applied Physics (JJAP), Vol. 12, No. 10, October, 1973, pages 1585-1592.
In FIG. 2, I.sub.t represents a total injected current flowing through a path limited by the width W of the bottom of the ridge 51, I.sub.e represents a current which flows uniformly across the portion of the active layer 4 immediately beneath the ridge 51, and I.sub.o represents a leakage current which flows laterally (i.e. in directions parallel to the plane of the active layer 4) through portions other than those portions within the width W of the bottom of the ridge 51. Let it be assumed that the second cladding layer 5 has a thickness d.sub.CL and a resistivity .rho., that the thickness d.sub.CL is small relative to the width W, and further that the thickness of the active layer 4 is negligibly small.
The total current I.sub.t flowing through the ridge 51 is expressed by the following equation (1). EQU I.sub.t =I.sub.e +2 I.sub.o ( 1)
Assuming that the lateral direction is the y-axis, current -dI.sub.y flowing through the junction between locations y and y+.DELTA.y is expressed by the following equation (2). EQU -d I.sub.y =L.sub.c .multidot.J.sub.s .multidot.(exp(.beta.V.sub.y)-1)d.sub.y ( 2)
where:
L.sub.c is the resonator length, PA0 J.sub.x is the saturation current density, PA0 V.sub.y is the junction voltage at a position y in FIG. 2, and PA0 .beta. is equal to q/nKT, in which q is the elementary charge, k is the Boltzman constant, T is temperature, and n is assumed to be a generation/recombination current ratio that is usually equal to 2. PA0 I.sub.y is current flowing at the location y in the y-axis direction, and PA0 .rho..sub.y is a value expressed as .rho..sub.y =.rho./(L.sub.C .times.d.sub.CL), in which, as stated previously, .rho. is the resistivity of the second cladding layer 5 and L.sub.C is the resonator length.
The voltage drop -dV.sub.y in the second cladding layer 5 is expressed by the following equation (3). EQU -d V.sub.y =.rho..sub.y .multidot.I.sub.y .multidot.d.sub.y ( 3)
wherein
Assuming that exp(.beta.V.sub.y)&gt;&gt;1 (the assumption being always true in this technical field), the following equation (4) can be derived from the equations (2) and (3). ##EQU1## The solution of the equation (4) is ##EQU2## where l.sub.o =2/(.beta..multidot..rho..sub.y .multidot.I.sub.o).
The current flowing through the junction between y and y+.DELTA.y, expressed as a function of y, .DELTA.I.sub.j (y), can be expressed, using the equation (5), by the following equation (6). ##EQU3##
Since current I.sub.j (0) at the bottom of the ridge having a width W is I.sub.e, ##EQU4##
Substituting the equation (7) into the equation (1), the following equation (8) results. ##EQU5## Solving the equation (8) with respect to I.sub.o, the following equation (9) is derived. ##EQU6##
As described above, I.sub.o represents a leakage current flowing in the y-axis direction which is in parallel with the plane of the active layer 4. The magnitude of the leakage current I.sub.o is largely dependent on .rho..sub.y and, hence, on the resistivity .rho. and the thickness d.sub.CL of the second cladding layer 5, as is understood from the equation (9).
Let it be assumed that the thickness of the second cladding layer 5, d.sub.CL =0.25 .mu.m and the resistivity .rho.=0.05 .OMEGA..multidot.cm. When the resonator length L.sub.C =250 .mu.m, the actual total injected current I.sub.t will contain a leakage current of about 40%. When the resistivity .rho. of the second cladding layer 5 is 0.08 .OMEGA..multidot.cm, with the other conditions maintained the same as the above, the percentage of the leakage current I.sub.o in the total injected current I.sub.t will be reduced to about 35%.
As will be understood from the above explanation, in the conventional semiconductor laser device shown in FIG. 1, the leakage current I.sub.o is largely dependent on the thickness and resistivity of the second cladding layer 5. In order to reduce the leakage current I.sub.o, a higher resistivity .rho. could be employed for the second cladding layer 5. However, when a high resistivity .rho. second cladding layer is used, the resistance of the device increases and, accordingly, heat generated by the device also increases, which is not desirable for a semiconductor laser device.
The object of the present invention is to eliminate the above-mentioned problem seen in conventional semiconductor devices as described above, by providing a semiconductor laser device having its resistance minimized as much as possible and having a reduced leakage current component I.sub.o.